It has been of significant importance to provision network-wide guaranteed QoS for a wide range of event detection applications in wireless sensor networks (WSNs). This paper investigates solutions to this QoS provision problem. For event detection applications, there are two key performance metrics, i.e., detection probability and detection latency. This paper focuses on dual-objective QoS provision, taking both metrics into account. This is very challenging due to the stringent resource constraint of sensor nodes and unpredictable randomness of physical events. We propose a novel probabilistic approach to provisioning due-objective QoS. Following a unified framework, we design a distributed algorithm that determines the active probability of every sensor node. The probability is minimized while being sufficient for QoS provision. Our approach is flexible and supports different requirements that may be posed by different applications. Theoretical analysis and comprehensive simulation experiments have been conducted, which jointly demonstrate that our approach is able to deliver guaranteed QoS for distributed event detection while prolonging the system lifetime significantly compared with other alternative schemes.